it is not advisable to make only the minimum payment on a credit card if Jason wants to minimize the amount of interest he has to pay and pay off his debt faster.
What is Credit card?A credit card is a payment card issued to users to enable the cardholder to pay a merchant for goods and services based on the cardholder's accrued debt.
Jason may not be doing the right thing by making only the minimum payment on his credit card, depending on the interest rate and penalty charges.
When a credit card holder makes only the minimum payment, the remaining balance accrues interest, which is added to the principal amount.
This means that the total amount owed on the credit card increases every month, even if no additional purchases are made.
The interest rate charged by the credit card company can significantly impact how much Jason ends up paying over time.
Hence, it is not advisable to make only the minimum payment on a credit card if Jason wants to minimize the amount of interest he has to pay and pay off his debt faster.
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explain why the two triangles are similar, then find the length x pls help I need in it like an hour
The two angels are similar because they have the same magnitude of corresponding angles. The length of x is 6 cm.
How are the conditions for similar triangles?For two or more similar triangles, it has two conditions.
Corresponding angles of the triangles are equal.Corresponding sides of the triangles are in proportion to each other.The two triangles as shown in the picture, ΔABC and ΔEDC.
Explain why the two triangles are similar! Find the length of x!
We have
AB = 1.8 kmAC = 3 kmBC = 2 kmm∠A = m∠ECE = 10 kmCD = xThe magnitude of ∠BCA and ∠DCE are equal. It is because they are at one point of intersection.
Since, ∠BCA and ∠DCE are equal and m∠A = m∠E, the other angles are also same.
Thus, the two triangle are similar. They have the same magnitude of corresponding angles.
Then, we find x. See the picture in the attachment!
3/10 = 1.8/x
x = (10 × 1.8)/3
x = 18/3
x = 6 cm
Hence, they are similar because they have the same corresponding angles. The x has the length of 6 cm.
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Albinism in humans is autosomal and fully recessive to normal color. A couple, who are both normal, have a daughter who is albino and a son who is normal. The couple wants to have 3 more children. What is the probability that they will have 3 normal girls?
The probability that the couple will have 3 normal girls is approximately 0.422
Since both parents are normal, they both have to be heterozygous carriers for the recessive allele that causes albinism. We can represent the normal allele with the letter N and the albino allele with the letter n. Then, we can write the genotypes of the parents as Nn x Nn.
The daughter is albino, so her genotype must be nn. The son is normal, so his genotype must be Nn.
We want to find the probability that the couple will have 3 normal girls. We can use the multiplication rule of probability to find this probability:
P(3 normal girls) = P(normal girl) x P(normal girl) x P(normal girl)
The probability of having a normal girl is 3/4 since there are three possible genotypes that result in a normal phenotype (NN, Nn, Nn) out of a total of four possible genotypes. The probability of having a normal boy is also 3/4, for the same reason.
Therefore, the probability of having 3 normal children (in this case, girls) is:
P(3 normal girls) = (3/4) x (3/4) x (3/4) = 27/64 ≈ 0.422
So, the probability that the couple will have 3 normal girls is approximately 0.422, or about 42.2%.
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Find the sum and express it in simplest form.
(-3n³-3n²) + (8n³ + 6n² - 4)
Answer:
= 5n³ + 3n² - 4
Step-by-step explanation:
(-3n³-3n²) + (8n³ + 6n² - 4)
= -3n³-3n²+8n³+6n²-4
= -3n³+8n³-3n²+6n²-4
= 5n³+3n²-4.
A game is played in which a card is randomly drawn from a well-shuffled standard deck of 52 cards. The card is recorded and then returned to the deck. Another card is drawn and the process is repeated 10 times. Let K =the number of kings observed in the 10 trials. Note that there are four kings in a standard deck of 52 cards.
A. Calculate and interpret the mean of K. b. Calculate and interpret the standard deviation of K.
B. Calculate and interpret the standard deviation of K
C. What is the probability of getting more than 4 kings?
D. Compute P(K≤ 3).
E. As described, this setting is binomial. Describe a setting using a well-shuffled standard deck of 52 cards that would not be binomial. Briefly explain your reasoning.
As a result of answering the question, we may state that equation In ten attempts, there is a 0.0407 percent chance of getting more than four kings, which is a very little chance.
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals symbol (=). A theoretical statement that proves the equality of two formulas is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14.
A. With n=10 and p=4/52, the binomial distribution of the number of kings seen in the 10 trials, K, is followed (since there are 4 kings in a standard deck of 52 cards). K's average is:
mean(K) is equal to[tex]n * p (10 * 4/52 = 0.7692).[/tex]
Meaning: On average, we anticipate seeing 0.77 kings per 10 trials.
B. This is the variance of K:
The formula for var(K) is [tex]n * p * (1 - p) = 10 * 4/52 * (1 - 4/52) = 0.7255.[/tex]
K's standard deviation:
[tex]\sqrt(var(K)) = \sqrt(0.7255) = 0.8524[/tex] where sd(K) =
D. The binomial distribution can be used to calculate the likelihood of receiving more than four kings:
P(K > 4) = 1 - P(K 4) = 1 - 0.0407 for binom.cdf(4, 10, 4/52).
Interpretation: In ten attempts, there is a 0.0407 percent chance of getting more than four kings, which is a very little chance.
D. The binomial distribution can be used to get P(K 3):
Binom.cdf(3, 10, 4/52) = P(K 3) = 0.8789
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Help me pls asap …..
Based on the information, it can be inferred that the volume of a cube with a side length of 30 cm is 27,000cm³ and the area would be 90cm².
How to calculate the volume and area of the cube?To calculate the volume and area of the cube we must perform the following mathematical procedures:
Volume:
We must multiply side * base * depth = volume.
30cm * 30cm * 30cm = 27,000cm³Area:
We must multiply the base by the side
30cm * 30cm = 90cm²According to the above, the area and volume of this cube would be 90cm² and 27,000cm³ respectively.
Note: This question is incomplete. Here is the complete information:
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What values of x
and y
satisfy the system {y=−2x+3
{y=5x−4?
Enter your answer as an ordered pair, like this: (42, 53)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The solution to the system of equation y = -2x + 3 and y = 5x - 4 is (1,1).
What is the solution to the system of equation?Given the system of equation in the question;
y = -2x + 3
y = 5x - 4
To solve the system of equation, plug equation one to into equation two and solve for x.
y = 5x - 4
Plug in y = -2x + 3
-2x + 3 = 5x - 4
Solve for x
-2x - 5x = - 4 - 3
-7x = -7
x = -7 / -7
x = 1
Now, plug x = 1 into equation one and solve for x.
y = -2x + 3
Plug in x = 1
y = -2( 1 ) + 3
y = -2 + 3
y = 1
Therefore, the value of x is 1 and y is also 1.
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if given two numbers of the following forms, which ones do not result in the correct mathematical result in the same form? assume there is no overflow (i.e., the result can fit in the available wires).
The two numbers of the form a+bi and c+di where a,b,c, and d are real numbers, and i is the imaginary unit, always resulting in the correct mathematical result in the same form.
This is because complex numbers are a mathematical construct and the operations defined on them, such as addition, subtraction, multiplication, and division, follow the rules of arithmetic. These operations preserve the form of the numbers, so that the result of any two complex numbers, when operated upon, will always be in the form of a complex number.
For example, when adding two complex numbers (a + bi) and (c + di), the real parts add up to form a new real part, and the imaginary parts add up to form a new imaginary part, resulting in a new complex number in the form (a + c) + (b + d)i.
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Find x in the right triangle
The solution is, the value of x=4.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
here, we have,
We can modify the Pythagorean Theorem to fit our needs and solve x. We know our c and our a so to find x or b
we use c^2-a^2=b^2.
from the given figure , we get,
Lets input our known.
5^2-3^2=x^2.
Lets start solving by squaring.
25-9=x^2
Subtract
16=x^2
Take the square root
4=x
Hence, The solution is, the value of x=4.
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Suppose a basketball player makes 55.3% of shots and that the probability of making each shot is independent. If the basketball player attempts 6 shots, what is the probability of making at least one shot?
There is a probability of 98.1% or around 0.98 of making at least one shot.
We can solve this problem using the binomial distribution. Let X be the number of shots the basketball player makes out of 6 attempts. Then X follows a binomial distribution with parameters n = 6 (number of trials) and p = 0.553 (probability of success).
The probability of making at least one shot can be calculated as the complement of the probability of missing all six shots. That is:
P(X ≥ 1) = 1 - P(X = 0)
Using the binomial probability formula, we can calculate P(X = 0) as:
P(X = 0) = (6 choose 0) * (0.553)^0 * (1 - 0.553)^(6-0) = 0.019
where (6 choose 0) = 1 is the number of ways to choose 0 shots out of 6.
Therefore,
P(X ≥ 1) = 1 - P(X = 0) = 1 - 0.019 = 0.981
So the probability of making at least one shot is approximately 0.981 or 98.1%.
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If A is a set{x,y,z} what is the power set, P(A)?
The power set P(A) is P(A) = { {}, {x}, {y}, {z}, {x,y}, {x,z}, {y,z}, {x,y,z} }
How to determine the power set P(A)The power set of a set A is the set of all subsets of A, including the empty set and A itself.
For the set A = {x, y, z}, the possible subsets are:
Empty set: {}Set containing only x: {x}Set containing only y: {y}Set containing only z: {z}Set containing x and y: {x, y}Set containing x and z: {x, z}Set containing y and z: {y, z}Set containing x, y, and z: {x, y, z}Therefore, the power set of A, denoted P(A), is:
P(A) = { {}, {x}, {y}, {z}, {x,y}, {x,z}, {y,z}, {x,y,z} }
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In Problems 37 through 42, determine by inspection at least one solution of the given differential equation. That is, use your knowledge of derivatives to make an intelligent guess. Then test your hypothesis. 37. y" = 0 38. y' = y 39. xy' + y = 3x2 40. (y')2 + y2 = 1 41. y' + y = ex 42. y" + y = 0
Previous question
37. A possible solution is y(x) = ax + b, where a and b are constants. Taking two derivatives gives y''(x) = 0, which satisfies the differential equation.
38. A possible solution is y(x) = Ce^x, where C is a constant. Taking the derivative of y(x) gives y'(x) = Ce^x, which satisfies the differential equation.
39. A possible solution is y(x) = 3 + 2x^2, which can be checked by taking the derivative and plugging it into the differential equation: xy'(x) + y(x) = x(4x) + (3 + 2x^2) = 3x^2 + 2x^2 + 3 = 5x^2 + 3, which is equal to 3x^2 when x=0.
40. A possible solution is y(x) = sin(x), which can be checked by taking the derivative and plugging it into the differential equation: (y'(x))^2 + (y(x))^2 = cos^2(x) + sin^2(x) = 1.
41. A possible solution is y(x) = ex - 1, which can be checked by taking the derivative and plugging it into the differential equation: y'(x) + y(x) = e^x + e^x - 1 = 2e^x - 1.
42. A possible solution is y(x) = Asin(x) + Bcos(x), where A and B are constants. Taking the second derivative gives y''(x) = -Asin(x) - Bcos(x), which satisfies the differential equation.
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What is the area of the trapezoid?
8 cm-8 cm-8 cm
10 cm
The area of the trapezoid is given as follows:
160 cm².
How to obtain the area of a trapezoid?The area of a trapezoid is obtained adding the bases, multiplying by the height, and dividing by 2.
For the trapezoid in this problem, the parameters are given as follows:
Bases 8 and 24 cm.Height of 10 cm.Hence the area is given as follows:
A = 0.5 x (8 + 24) x 10
A = 160 cm².
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What is the length of XZ? Step by step.
The measure of XZ is equivalent to 24. Option C is correct
Solving similar trianglesThe given triangles in question are similar in nature. For every similar triangles, the ratio of the similar sides of the triangle is equal to a constant as shown:
k+3/36 = k+5/44
Cross multiply and expand
36(k + 5) = 44(k + 3)
36k + 180 = 44k + 132
36k - 44k = 132-180|
-8k = -48
k = 6
For the measure of XZ
k/XZ = k+5/44
6/XZ = 11/44
6/XZ = 1/4
XZ = 24
Hence the measure of XZ from the given diagram is equivalent to 24
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mack is selling beaded necklaces and beaded wristbands at the craft market. a. a necklace requires 40 minutes to make. b. a wristband requires 25 minutes to make. c. mack has 360 minutes to make the necklaces and wristbands. additionally, a. mack wants to make no more than 12 items. b. when mack sells the necklaces and wristbands at the craft market, he will make $3.00 profit per necklace and $2.00 profit per wristband. let x = the number of necklaces mack maker.
Let y = the number of wristbands mack makes.
Mack should make 4 necklaces and 8 wristbands to maximize his profit while staying within his time and quantity constraints.
His profit would be:
Profit = 3(4) + 2(8) = $20.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.
From the information given, we know:
a) Necklace requires 40 minutes to make.
Let x be the number of necklaces made, then the total time spent on necklaces is 40x.
b) Wristband requires 25 minutes to make.
Let y be the number of wristbands made, then the total time spent on wristbands is 25y.
c) Mack has a total of 360 minutes to make necklaces and wristbands. Therefore, the equation for time is:
40x + 25y = 360
d) Mack wants to make no more than 12 items, so we have the inequality:
x + y ≤ 12
e) Mack makes a profit of $3.00 per necklace and $2.00 per wristband. Therefore, the equation for profit is:
Profit = 3x + 2y
Now we have the following system of equations:
40x + 25y = 360
x + y ≤ 12
Profit = 3x + 2y
From equation (2), we have y = 12 - x.
Substitute y = 12 - x into equations (1) and (3):
40x + 25(12 - x) = 360
Profit = 3x + 2(12 - x)
Simplify and solve for x:
40x + 300 - 25x = 360
15x = 60
x = 4
Substitute x = 4 into equation (2) to find y:
y = 12 - x = 12 - 4 = 8
Therefore, His profit would be, Profit = 3(4) + 2(8) = $20.
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which statement describes the relationship between X and Y in these two equations y = 2x Y = X + 2
The relationship between X and Y in the equations y = 2x and y = x + 2 is that they represent two different linear equations.
How to describe the relationship in the equationsFrom the question, we have the following parameters that can be used in our computation:
y = 2x
y = x + 2
Using the above as a guide, we have the following:
The equations are linear equationsThe linear equations are not equivalentHence, the relationship is different linear equations
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(x − 3)(x² - 7x - 2)
Answer:
[tex]\huge\boxed{\sf x\³ - 10x\² + 19x + 6}[/tex]
Step-by-step explanation:
Given expression:= (x - 3)(x² - 7x - 2)
Distribute= x(x² - 7x - 2) - 3(x² - 7x - 2)
= x³ - 7x² - 2x - 3x² + 21x + 6
Combine like terms= x³ - 7x² - 3x² - 2x + 21x + 6
= x³ - 10x² + 19x + 6[tex]\rule[225]{225}{2}[/tex]
Answer these five questions from the triangle ABC
1. ~ ABC=
2. AB/AD=BC/?
3. 3/9=x/?
4. x=
5. scale factor of ADE to ABC
Please give full answers
Answer:
1. ~ ABC = 180 degrees
2. AB/AD = BC/AC
3. 3/9 = x/6
4. x = 2
5. The scale factor of ADE to ABC is 1:2.
Step-by-step explanation:
1. ~ABC = 180 degrees means that the sum of all the angles of a triangle add up to 180 degrees.
2. AB/AD = BC/AC means that if two sides of a triangle are divided by another side, the ratio will be the same for both sides of the triangle.
3. 3/9 = x/6 means that if you divide 3 by 9, you can find out what x is when it is divided by 6.
4. x = 2 means that when 3 is divided by 9 and the result is divided by 6, the answer is 2.
5. The scale factor of ADE to ABC is 1:2 means that ADE is twice the size of ABC and all related measurements between the two triangles are in a proportion of 1:2.
surface area
42 in.
11 in.
21 in
Answer:
3150
Step-by-step explanation:
...2(42x11+21x11+42x21)
BTW: This isn´t college-level math this is like 2nd-grade math.
Please solve quickly! Within 30 minutes would be great!
Please solve for the variable indicated.
A=1/2bh(h+b), solve for h
If you could break it down step by step that would be super helpful! I’m very confused. Thank you!
The equation solved for the variable h is h = [tex]\sqrt[]{\frac{2A -b^2}{b} }[/tex]
How to determine the subject of formulaTo solve for a variable in a given equation is to make it the subject of formula.
The variable is made to stand alone on one end of the equality sign.
We have the equation given as;
A=1/2bh(h+b)
First, cross multiply
2A = bh(h+b)
2A = bh² + b²
collect like terms
2A - b² = bh²
Now divide by the coefficient of h²
h² = 2A - b²/b
Find the square root of both sides
h = [tex]\sqrt[]{\frac{2A -b^2}{b} }[/tex]
Hence, the equation is h = [tex]\sqrt[]{\frac{2A -b^2}{b} }[/tex]
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help please
i give brainliest
Determine which of the vectors is (are) parallel to z_ Use a graphing utility to confirm your results. (Select all that apply.) z has initial point (5, 4, 1) and terminal point (-2, -4, 4). a. 7i + 6j + 2k
b. -7i- 6j -2k c. 14i +16j+ 6k d. -14i -16j + 6k
e. i + 4j - 2k f. i - 4j + 2k g. None of these vectors are parallel to z.
The vectors that are parallel to z that has has initial point (5, 4, 1) and terminal point (-2, -4, 4) are -7i - 6j - 2k and -14i - 16j + 6k. So, the correct options are B and D.
To determine which vectors are parallel to z, we need to compare their direction to the direction of z. Two vectors are parallel if they have the same direction or are opposite in direction.
The direction of z can be found by subtracting the initial point from the terminal point:
z = (-2 - 5)i + (-4 - 4)j + (4 - 1)k
z = -7i - 8j + 3k
Now let's compare the direction of each given vector to the direction of z:
a. 7i + 6j + 2k: This vector is not parallel to z because it has a different direction.
b. -7i- 6j -2k: This vector is parallel to z because it has the opposite direction.
c. 14i +16j+ 6k: This vector is not parallel to z because it has a different direction.
d. -14i -16j + 6k: This vector is parallel to z because it has the opposite direction.
e. i + 4j - 2k: This vector is not parallel to z because it has a different direction.
f. i - 4j + 2k: This vector is not parallel to z because it has a different direction.
Therefore, the vectors that are parallel to z are b. -7i - 6j - 2k and d. -14i - 16j + 6k.
To confirm these results using a graphing utility, we can plot z and each of the given vectors on a 3D coordinate system and visually check their directions.
Here is an example using Wolfram Alpha:
vectorplot3d {<-7, -8, 3>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}
vectorplot3d {<7, 6, 2>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}
vectorplot3d {<-7, -6, -2>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}
vectorplot3d {<14, 16, 6>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}
vectorplot3d {<-14, -16, 6>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}
vectorplot3d {<1, 4, -2>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}
vectorplot3d {<1, -4, 2>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}
This will generate a 3D plot with all the vectors plotted. We can see that only the vectors with opposite directions to z, namely -7i - 6j - 2k and -14i - 16j + 6k, are parallel to z.
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A tree is struck by lightning and snaps off 34 feet above the ground. The top part of the tree comes to rest creating a 17-degree angle with the ground. How tall was the tree before it broke to the nearest tenth of a foot?
We conclude that the angle at the top measures 65.8°.
What is right angle triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangled triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry.
here, we have,
What angle does the top part?
The whole tree measures 117 ft, and it is broken 34 ft above the ground, forming this way a right triangle.
Then one cathetus of the right triangle measures 34ft, and the hypotenuse measures 117ft - 34ft = 83ft
The angle at the top is θ, the adjacent cathetus to it is the one that measures 34 ft, then to get the angle we can use the relation:
cos(θ) = (adjacent cathetus)/(hypotenuse)
Replacing what we know, we get:
cos(θ) = (34 ft)/(83ft) = 34/83
Solving for θ, we get:
θ = Acos( 34/83) = 65.8°
So we conclude that the angle at the top measures 65.8°.
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Charlotte and Pablo are each making purple paint by mixing blue
paint and red paint. Charlotte uses 1 cup of red paint for every
2 cups of blue paint. Pablo uses 2 cups of red paint for every
3 cups of blue paint. Whose paint is a bluer shade of purple?
Answer:
Charlotte's mix has a bluer shade of purple
Step-by-step explanation:
Since we are asked whose paint is a bluer shade it would be easier to express the ratios of the paint mix as blue:red
Charlotte: 1 cup red for every 2 cups blue ==> 2 cups blue for every 1 cup red
This can be expressed as the ratio
[tex]\dfrac{ 2 \;blue}{1\;red} = \dfrac{2}{1} = 2[/tex]
[tex]-------------------[/tex]
Pablo : 2 cups red for every 3 cups blue ==> 3 cups blue for every 2 cups red
The ratio of blue to red
= [tex]\dfrac{3 \;blue}{2\;red} = \dfrac{3}{2} = 1\dfrac{1}{2} \;\; (or\; 1.5)[/tex]
Since
[tex]2 > 1\dfrac{1}{2} \;\;\;(or\; 2 > 1.5)[/tex]
Charlotte's mix has a bluer shade of purple
evaluate the following: f open parentheses x close parentheses equals 3 x squared minus 2 x plus 1 comma space e v a l u a t e space f open parentheses negative 1 close parentheses
The value of the function f(x) = 3x^2 - 2x + 1 at x = -1, will be 6
In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.
Algebraic expressions are expressions that are made up of variables and constants. Any value can be assigned to a variable. The value of an expression changes depending on the values assigned to the variables it includes. There are an unlimited number of points on a number line.
To evaluate the function f(x) = 3x^2 - 2x + 1 at x = -1,
we simply substitute -1 for x in the expression:
f(-1) = 3(-1)^2 - 2(-1) + 1
= 3(1) + 2 + 1
= 6
Therefore, f(-1) = 6.
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¿ Como despejar B en esta variable
The simplified form of the expression (4 - a²b³)/5 = (9 - 3b³)/7 is
b³(15 - 7a²) = 17.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, An equation (4 - a²b³)/5 = (9 - 3b³)/7, in variables 'a' and 'b'.
7(4 - a²b³) = 5(9 - 3b³).
28 - 7a²b³ = 45 - 15b³.
15b³ - 7a²b³ = 45 - 28.
b³(15 - 7a²) = 17.
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Choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions. h k a. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.)
The system has no solution only when h = 3 and k ≠ 20.
The system has unique solution when h ≠ 3 and k is any real number.
System has many solutions only when h = 3 and k = 20
As per the data given:
[tex]& x_1+h x_2=5 \\[/tex]
[tex]& h x_1+12 x_2=k[/tex]
Consider augmented matrix
[tex]\quad[A \mid b]= & {\left[\begin{array}{cc|c}1 & h & 5 \\h & 12 & k\end{array}\right] } \\[/tex]
[tex]R_2 \rightarrow R_2-4 R_1 & {\left[\begin{array}{cc|c}1 & h & 5 \\0 & 12-4 h & k-20 \\\end{array}\right] }\end{aligned}[/tex]
(a) System has no solution if rank(A) ≠ rank(A|b)
Therefore if 12 - hk = 0 and k - 20 ≠ 0 then
rank(A) ≠ rank(A|b) and system has no solution
12 = 4h and k ≠ 20
h = 3 and k ≠ 20
Answer: E. The system has no solution only when h = 3 and k ≠ 20.
(b) The system has unique solution if rank(A) = rank(A|b)
Number of variables = 2
This is possible only when 12 ≠ 4h and h ≠ 3
The system has unique solution when h ≠ 3 and k is any real number.
(c) The system has many solution when rank(A) = rank(A|b) ≤ (Number of variables = 2)
Therefore this is true only when 12 - 4h = 0 and k - 20 = 0 i.e. h = 3 and k = 20
System has many solutions only when h = 3 and k = 20
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Choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions.
[tex]x_1+h x_2=5 \\[/tex]
[tex]4 x_1+12 x_2=k[/tex]
a. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.)
A. The system has no solutions only when [tex]$k \neq \square$[/tex] and h is any real number.
B. The system has no solutions only when h = [tex]\square$[/tex] and k=
C. The system has no solutions only when h [tex]\neq \square$[/tex] and [tex]$k \neq$[/tex]
D. The system has no solutions only when [tex]$\mathrm{h}=\square$[/tex] and k is any real number.
E. The system has no solutions only when [tex]$h=\square$[/tex] and [tex]$k \neq$[/tex]
F. The system has no solutions only when [tex]$k=\square$[/tex] and h is any real number.
G. The system has no solutions only when [tex]$h \neq \square$[/tex] and k is any real number.
H. The system has no solutions only when [tex]$h \neq \square$[/tex] and k= ___
Help please I’m dying and it is dew tomorrow and I have no clue what it could be
The effect on the graph for the given function if the slope of the function is changed to -10 include the following: D. the line is less steep.
The effect on the graph for the given function if the y-intercept of the function is changed to a smaller positive number is: C. the line shifts down.
What is a slope?In Mathematics, a slope is sometimes referred to as rate of change and it is typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.
Generally speaking, a slope simply refers to a measure of the steepness of a straight line. This ultimately implies that, the higher the slope of a line, the more steep it is and vice-versa.
Based on the information provided about this function y = 8 - 2x, we can logically deduce that the line would be shifted downward when its y-intercept is changed to a smaller positive number.
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8 ft. 3 ft. is what in geometry
In geometry, 8 ft. 3 ft. specifies the dimension of an object. That is the length and the width.
What does 8 ft. 3 ft means means in geometry?
8 ft. 3 ft. is a dimension, specifically a length and a width. It could refer to the size of a rectangular object, such as a room or a piece of furniture.
In geometry, such a dimension is often used to calculate the area of the rectangle.
The area of a rectangle can be found by multiplying its length by its width.
So, in this case, the area of the rectangle with dimensions 8 ft. * 3 ft. would be 8 ft * 3 ft = 24 ft².
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Use the remainder theorem and synthetic division to find the value of
f(3) if f(3) = x^3 - 6x^2 + 13x - 11
SHOW THE STEPS OF THE SYNTHETIC DIVISION!
The quotient is x² - 3 - 4 and remainder is 1.
So, The value of f (3) is, 1
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
The value of f(3) is told by the remainder theorem to be the remainder from division of f(x) by (x -3). That division is shown in the attachment. The remainder is 1, hence we have;
⇒ f(3) = 1
The number at upper left in the synthetic division table is the value of x for which we are evaluating f(x).
When the polynomial is written in Horner Form:
⇒ f(x) = ((x -6)x +13)x -11
Here, the coefficient of x at each point in the evaluation is the same as the number on the bottom row of the synthetic division. The result of the evaluation is the same as the remainder from the division.
Now, Add the obtained result to the next coefficient of the dividend and write down the sum as;
3 | 1 - 6 13 - 11
3 - 9 3x4 = 12
-----------------------
1 - 3 4 (- 11) + 12 = 1
Thus, We have complete table and have obtained the resulting coefficient are,
1 , - 3, 4, 1
Thus, The quotient is x² - 3 - 4 and remainder is 1.
So, The value of f (3) is, 1
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A box contains 24 tiles. Each tile has certain properties:
Each tile is made of wood or plastic.
Each tile is red, yellow, or blue.
Each tile is a triangle, square, pentagon, or circle.
There is exactly one tile for each combination of properties. For example, there is one red circle that is made of wood.
Steve chooses one tile, and Ellen chooses a different tile.
What is the probability that both tiles are red?
Answer: 12
Step-by-step explanation: